WEBVTT
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we're going to evaluate this difference quotient for the function
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F of X equals one over X notice that we
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need to know f of a so f of a
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is going to be one over a. Okay,
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so now let's substitute F of X one over X
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into our quotient and f of a one over a
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into our quotient, and that's over X minus a
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. So here's the question that we're hoping to simplify
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. And any time you have a complex fraction like
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this where you have fractions inside your fraction, it's
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a good idea to multiply by a special form of
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one to clear those fractions. So I'm going to
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multiply the top and bottom by X times. A
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. I'm just gonna put that over one so that
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everything lines up nicely. So what happens then is
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when we multiply one over X by X times a
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The X's cancel and we just have a minus.
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Now we multiply one over a by X Times A
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and the A's council, and we just have X
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. And then that's over. X minus a times
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X times a Nothing councils there, so I'm just
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going to call that X a times the quantity X
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minus a. Okay, let's look at what we
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have now. Notice that we have a minus X
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on the top and we have X minus A on
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the bottom. Those are opposites. And we can
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cancel opposites if we leave negative one. Just like
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we can cancel things that are equivalent if we leave
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positive one or the other way to think about it
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is just factor a negative one out of the numerator
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and it will be negative one times a quantity X
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minus a And now you can just cancel your X
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minus ace. So what do we have now?
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We have negative one over X times A. You
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could call it eight times X or x times a
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.